Problem: Divide the polynomials. The form of your answer should either be $p(x)$ or $p(x)+\dfrac{k}{x+3}$ where $p(x)$ is a polynomial and $k$ is an integer. $\dfrac{2x^3-x^2-12}{x+3}=$
Usually, there are many different ways to divide polynomials. Here, we will use the method of polynomial long division. Notice that the expression in the numerator is missing a $1^{\text{st}}$ degree term. To avoid any confusion, let's add that term as $0x$. $\begin{array}{r} 2x^2-\phantom{1}7x+21 \\ x+3|\overline{2x^3-\phantom{6}x^2+\phantom{0}0x-12} \\ \mathllap{-(}\underline{2x^3+6x^2\phantom{-28x-12}\rlap )} \\ -7x^2+\phantom{0}0x-12 \\ \mathllap{-(}\underline{-7x^2-21x\phantom{-12}\rlap )} \\ 21x-12 \\ \mathllap{-(}\underline{21x+63\rlap )} \\ -75 \end{array}$ We found that the quotient is $2x^2-7x+21$ and the remainder is $-75$ : $\dfrac{2x^3-x^2-12}{x+3}=2x^2-7x+21-\dfrac{75}{x+3}$